Complex network construction method based on adjacent matrixes

Abstract

The invention discloses a complex network construction method based on adjacent matrixes. A complex network is constructed based on a Kronecker multiplication operation and a Kronecker addition operation generating network adjacent matrixes. The method comprises the main steps of determining the generated network, calculating the generated network adjacent matrixes, calculating a generated network degree distribution polynomial, calculating the adjacent matrixes of the complex network, calculating the degree distribution polynomial of the complex network and the like. The complex network obtained through the complex network construction method is different from a classical stochastic network, a small-world network, a scale-free network, a self-similarity network and the other networks. By the adoption of the degree distribution polynomial expression method, according to the Kronecker addition operation, the operation of coefficient addition and frequency multiplication of normal polynomial multiplication is adopted; according to the Kronecker addition operation, the operation of coefficient addition and frequency multiplication of similar polynomial multiplication is adopted, and the complex network degree distribution is worked out strictly in theory. Particularly, the self-similarity network can be obtained based on the Kronecker multiplication operation generating the network adjacent matrixes.

Description

technical field [0001] The invention belongs to the field of electrical digital data processing, and is particularly suitable for a data processing method with specific functions, in particular to a complex network construction method based on a Kronecker sum operation and Kronecker product operation for simply generating a network adjacency matrix. Background technique [0002] The in-depth study of complex networks has promoted the rise of network science, and research objects in many fields such as natural sciences and social sciences can be abstracted into complex networks for research. The construction of complex network model occupies an extremely important position in the analysis and research of social network, computer network, virtual social network and other fields. In the middle of the last century, the introduction of the ER random network model initiated the systematic study of complex networks, and led the subsequent research on complex networks for nearly hal...

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Problems solved by technology

[0011] Generally speaking, the research on the characteristics of complex networks is still a hot spot in complex network research today. It is undeniable that although there are relatively mature theories on random networks, small-world networks, scale-free networks and self-similar networks, etc. and methods, most of the studies are also consistent with real complex networks, but still cannot fully reflect the various characteristics of real complex networks in real life, and further research on the characteristics of complex networks is required

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